Solve for $x$ : $4\sqrt{x} - 8 = 7\sqrt{x} + 5$
Answer: Subtract $4\sqrt{x}$ from both sides: $(4\sqrt{x} - 8) - 4\sqrt{x} = (7\sqrt{x} + 5) - 4\sqrt{x}$ $-8 = 3\sqrt{x} + 5$ Subtract $5$ from both sides: $-8 - 5 = (3\sqrt{x} + 5) - 5$ $-13 = 3\sqrt{x}$ Divide both sides by $3$ $\frac{-13}{3} = \frac{3\sqrt{x}}{3}$ Simplify. $-\dfrac{13}{3} = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.